Abstract:
The viscous flow in the outer core induced by inner core rotation relative to the mantle is computed under the geostrophic approximation for a simple Earth model having a homogeneous, incompressible and viscous outer core. The mantle, the inner core and their interfaces with the outer core are taken to be axially symmetric ellipsoids and the mantle is considered to be in uniform rotation about its symmetry axis. The inner core rotation relative to the mantle involves, in general, both a super-rotation and an inner core wobble (ICW). In the former, the component of the inner core angular velocity parallel to the mantle symmetry axis is higher than the angular velocity of rotation of the mantle itself; in the ICW, the symmetry axis of the inner core is inclined to that of the mantle and rotates around the latter. In both cases, the outer core flow outside the cylinder circumscribing the inner core and having its axis parallel to the mantle rotation axis is equivalent to a rigid rotation with the same angular velocity as that of the mantle. In the bulk of the region within the cylinder, the flow relative to the mantle is again a rotation around the mantle rotation axis, but with the angular rate varying continuously with distance from the rotation axis: from the rate of super-rotation itself at the surface of the cylinder, down to half that rate on the mantle rotation axis. The flows in the Ekman boundary layers at the inner core boundary (ICB) and at the core–mantle boundary (CMB) are also determined. The viscous torque exerted on the inner core is derived from the velocity field in the boundary layer, and its damping effects on the inner core super-rotation and the ICW are investigated. As various estimates found in the literature for the outer core viscosity differ by many orders of magnitude, numerical values of the Ekman depth and the damping time of inner core rotation are computed here for a few sample values.
